---
title: "Basic steps in finite element analysis"
subject: "Computational Techniques in Civil Engineering"
chapter: 1
key: "semester_8/computational_techniques_in_civil_engineering:fem-basic-steps"
source: https://www.bctengineer.com/q/semester_8/computational_techniques_in_civil_engineering/fem-basic-steps
site: BCT Engineering
---

# Basic steps in finite element analysis

Computational Techniques in Civil Engineering · Chapter 1: Introduction

- Asked in: 2077 Chaitra, 4 marks
- Video: [Basic Steps in FEA | Finite Element Analysis - 8 Steps | E3](https://www.youtube.com/watch?v=_ZBSdLZ53T0) — Msquare Analysis Projects
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/computational_techniques_in_civil_engineering/fem-basic-steps
- Whole chapter: https://www.bctengineer.com/md/semester_8/computational_techniques_in_civil_engineering/chapter-1

## Question

Describe the basic steps in finite element analysis.

## Short answer

FEM steps: discretise the body into elements and nodes; assume displacement shape functions; form strain and stress relations; derive element stiffness and load vectors; assemble global equations; apply boundary conditions; solve for nodal displacements; compute strains, stresses and reactions.

## Answer

The finite element method replaces a continuum by a finite number of elements and solves the resulting algebraic equations. The basic steps are:

1. **Discretisation:** divide the body into finite elements joined at nodes (select element type and mesh).
2. **Select interpolation (shape) functions:** assume displacement within an element as $u = [N]\{d\}$.
3. **Strain-displacement and stress-strain relations:** $\{\varepsilon\} = [B]\{d\}$, $\{\sigma\} = [D]\{\varepsilon\}$.
4. **Element stiffness matrix and load vector:** $[k] = \int [B]^T[D][B]\,dV$ and equivalent nodal loads $\{f\}$.
5. **Assembly:** combine element matrices into the global equations $[K]\{U\} = \{F\}$.
6. **Boundary conditions:** apply supports (known displacements) and loads.
7. **Solve** for nodal displacements.
8. **Post-processing:** compute strains, stresses, reactions and plot results.

```text
 Body -> Mesh -> [k] each -> [K]{U}={F} -> U -> stress
```

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the first step of finite element analysis?
   A. Assembly of global stiffness
   B. Solving for displacements
   C. Discretisation of the body into elements joined at nodes
   D. Post-processing
   Answer: C. The body is first divided into elements and nodes by selecting element type and mesh. (Key point: First step)

2. Which relations link nodal values to strain and stress?
   A. {strain} = [D]{d} and {stress} = [B]{strain}
   B. {strain} = [B]{d} and {stress} = [D]{strain}
   C. {strain} = [N]{d}
   D. {stress} = [K]{U}
   Answer: B. [B] is the strain-displacement matrix and [D] the stress-strain matrix. (Key point: Strain relation)

3. What does assembly produce?
   A. The global equations [K]{U} = {F}
   B. The strains and stresses
   C. The shape functions
   D. The element mesh
   Answer: A. Element stiffness matrices and loads are combined into the global system. (Key point: Assembly)

4. What is done in the final step?
   A. Select interpolation functions
   B. Apply supports
   C. Form element stiffness
   D. Compute strains, stresses and reactions and plot results
   Answer: D. After solving for displacements, post-processing finds strains, stresses and reactions. (Key point: Post-processing)

## Related in Computational Techniques in Civil Engineering

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